# Tagged Questions

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### Is it decidable whether the iterates of a polynomial map are bounded?

Let $f:\mathbb{Q}^n\to \mathbb{Q}^n$ be a polynomial map with rational coefficients. Let $p\in \mathbb{Q}^n$. Is there a known algorithm that given this data determines whether or not the iterates ...
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### Diophantine equations and Hilbert's 10th Problem, how did MRDP do it?

I'm having a bit of trouble understanding the Wiki explanation of MRDP's (Matiyasevich, Robinson, Davis, Putnam)'s Theorem, which explains that Hilbert's 10th problem is unsolvable. The MRDP ...
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### Proving something is primitive recursive

I'm trying to prove $f(n) = 2n$ is primitive recursive. I understand that for something to be primitive recursive it must have the following properties: $0(x)=x$ the zero function $s(x)= x+1$ the ...
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### Show that $gcd(x,y)$ and $z = lcm(x,y)$ is primitive recursive

For the $gcd(x,y)$ we note: $gcd(x,0) = x$ $gcd(x,succ(y)) = gcd(succ(y),mod(x,succ(y)))$ $succ(x)$ and $mod(x,y)$ are both primitive recursive, so $gcd(x,y)$ must be as well. $z = lcm(x,y)$ if ...
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### Are transcendental numbers computable?

Wikipedia states: "The computable numbers include many of the specific real numbers which appear in practice, including all real algebraic numbers, as well as e, π, and many other transcendental ...
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### Subsets of all Diophantine's sets

Function $\mathbb{N}^k \to \mathbb{N}^m$ is computable $\Leftrightarrow$ graph of function is Diophantine. Consider some subset $S$ of computable functions (for example some Grzegorczyk's class or ...
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### Is discrete ultralogarithm harder than discrete logarithm?

Is computing $g^{xy} \bmod{s}$ from $g^{x} \bmod{s}$ and $g^{y} \bmod{s}$ easier harder or the same level of difficulty as computing $g\uparrow\uparrow(xy) \bmod s$ from from $g\uparrow\uparrow x$ ...
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### Post Correspondence Problem

The alphabet consists of just two characters, $0$ and $1$. How do I go about proving that it's undecidable? I was thinking of reducing the general case to binary form meaning if the alphabet has ...
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### Which diophantine polynomials generate these diophantine sets?

Via Matiyasevich's Theorem, it is easy to prove that the following sets are diophantine: $\{k\}$ $\{0, 1, \dots, k-1, k+1, k+2, \dots \}$ $\{0, 1, \dots, k\}$ $\{k+1, k+2, \dots\}$ Number 1 is ...
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